Solve the System of Equations y=x^2-8x+2 y=-2x+18

$y = x^{2} - 8 x + 2$ $y = - 2 x + 18$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} - 8 x + 2 = - 2 x + 18$

Step 2

Solve $x^{2} - 8 x + 2 = - 2 x + 18$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$x^{2} - 8 x + 2 + 2 x = 18$

Add $- 8 x$ and $2 x$ .

$x^{2} - 6 x + 2 = 18$

Subtract $18$ from both sides of the equation.

$x^{2} - 6 x + 2 - 18 = 0$

Subtract $18$ from $2$ .

$x^{2} - 6 x - 16 = 0$

Factor $x^{2} - 6 x - 16$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 16$ and whose sum is $- 6$ .

$- 8, 2 + y = - 2 x + 18$

Write the factored form using these integers.

$(x - 8) (x + 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x + 2 = 0 + y = - 2 x + 18$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $(x - 8) (x + 2) = 0$ true.

$x = 8, - 2$

Step 3

Evaluate $y$ when $x = 8$ .

Substitute $8$ for $x$ .

$y = - 2 \cdot 8 + 18$

Substitute $8$ for $x$ in $y = - 2 \cdot 8 + 18$ and solve for $y$ .

Remove parentheses.

$y = - 2 \cdot 8 + 18$

Simplify $- 2 \cdot 8 + 18$ .

Multiply $- 2$ by $8$ .

$y = - 16 + 18$

Add $- 16$ and $18$ .

$y = 2$

Step 4

Evaluate $y$ when $x = - 2$ .

Substitute $- 2$ for $x$ .

$y = - 2 \cdot - 2 + 18$

Substitute $- 2$ for $x$ in $y = - 2 \cdot - 2 + 18$ and solve for $y$ .

Remove parentheses.

$y = - 2 \cdot - 2 + 18$

Simplify $- 2 \cdot - 2 + 18$ .

Multiply $- 2$ by $- 2$ .

$y = 4 + 18$

Add $4$ and $18$ .

$y = 22$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(8, 2)$

$(- 2, 22)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, 2), (- 2, 22)$

Equation Form:

$x = 8, y = 2$

$x = - 2, y = 22$

Step 7

Solve the System of Equations y=x^2-8x+2 y=-2x+18

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